Hopefully someone else here likes Focus.

Anyway, I've seen Focus videos from the '70s - and Jan Akkerman has got a very strange guitar. It appears to be Gibson, by the headstock, and is very much like a Les Paul. But, it's too "beefy" for that. It's got what looks like a flametop, a one-piece wraparound bridge, and the end of the fretboard is slanted. I thought it was an L5S at first, but looking at it closer tells me it's not.

You can see it here and here.

Gibson I'd guess, as this picture of him in 2005 has a similar shaped guitar and it has the beefy headstock and slanted cut-off at the end of the fretboard.
Based on the Les Paul shape, the way the fretboard slants at the end of the neck, and the rounded lower horn, I'd say it looks like a Les Paul Recording Model.
Quote by Altered_Carbon
That's some bony hipster sex, which may be the best kind.
Can't help about the guitar, but I love that song. I remember when I first heard it on the radio a couple years ago and it infuriated the hell out of me because I didn't know who sang it and had no way to look it up...lol
If you're still here..

The guitar was originally a Les Paul Recording/Professional/Personal (same guitar), but he didn't like the pickups so he had them changed back into humbuckers, which left that edgy neck. He also had various other changes done to it. That's what I was told, from some quote I found after a million years of searching.
I collected Gibbys for a long time and there were a lot of strange versions I came across here and there and I questioned the authenticity but if you got the dough the custom shop will make you whatever you want especially if your a big name musician.

I doubt its a Recording LP I have a few and they had soap bar pups and a lot of knobs and switches. I never came across one with regular humbuckers and 3 at that. The body and neck look like a recording LP but the rest doesn't I'll bet it's a custom shop job.

This is indeed a 'Les Paul Personal'. Jan had it heavily modified by Paul Hamer in the early 70's. Pickups, wiring and that flame maple top onto the mahogany body. It got damaged and lay unused for 20 years and then Jan got it fixed up around 10 years ago and now plays it 50/50 with his famous Black Custom.
Have a look at this video of Sylvia - at 2'59" - 3'00"
A guess: it looks to me as though Jan Akkerman is playing what could be the pre-humbucker-modification version of a Les Paul 'Recording' - (perhaps with the pickup covers removed as you can see 6 poles) - he's got the control knobs down to 4 in the usual places.
(I played a friend's 'Recording' once, in 1970; I was 16 and had no idea of what I was holding.)